In Section 3.2 the GREEN's function for a system under equilibrium
at finite temperature has been introduced. In this section, a more general formalism
for systems under non-equilibrium conditions at finite temperature is presented.
First, the ensemble average of an operator under non-equilibrium is
defined. Then the contour-ordered non-equilibrium GREEN's function (NEGF)
formalism is introduced and the equation of motion for the GREEN's function is
presented. Finally, it will be shown that a perturbation expansion similar to
the equilibrium theory can be achieved.
3.3 Non-Equilibrium GREEN's Functions
M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors